Problem: $\dfrac{ -10c - 7d }{ -2 } = \dfrac{ c - 2e }{ -9 }$ Solve for $c$.
Solution: Multiply both sides by the left denominator. $\dfrac{ -10c - 7d }{ -{2} } = \dfrac{ c - 2e }{ -9 }$ $-{2} \cdot \dfrac{ -10c - 7d }{ -{2} } = -{2} \cdot \dfrac{ c - 2e }{ -9 }$ $-10c - 7d = -{2} \cdot \dfrac { c - 2e }{ -9 }$ Multiply both sides by the right denominator. $-10c - 7d = -2 \cdot \dfrac{ c - 2e }{ -{9} }$ $-{9} \cdot \left( -10c - 7d \right) = -{9} \cdot -2 \cdot \dfrac{ c - 2e }{ -{9} }$ $-{9} \cdot \left( -10c - 7d \right) = -2 \cdot \left( c - 2e \right)$ Distribute both sides $-{9} \cdot \left( -10c - 7d \right) = -{2} \cdot \left( c - 2e \right)$ ${90}c + {63}d = -{2}c + {4}e$ Combine $c$ terms on the left. ${90c} + 63d = -{2c} + 4e$ ${92c} + 63d = 4e$ Move the $d$ term to the right. $92c + {63d} = 4e$ $92c = 4e - {63d}$ Isolate $c$ by dividing both sides by its coefficient. ${92}c = 4e - 63d$ $c = \dfrac{ 4e - 63d }{ {92} }$